John Wallis was a founding member of the Royal Society, one of the oldest scientific organizations still in existence, and is considered by many the most influential British mathematician preceding Isaac Newton. He contributed the earliest forms, terms, and notations to nascent fields such as calculus and analysis. Wallis was the first to attempt to write a comprehensive history of British mathematics, striving to bring continuity to mathematical study and research. Among the many classical tracts Wallis translated and edited are two major works of Archimedes. He was also involved in government; as the Parliamentarians' cryptographer, Wallis was instrumental in deciphering enemy codes during the English Civil War. Not all of Wallis' discoveries were valid, as shown by the rare example of an attempt to analyze Euclid's fifth postulate in 1663 that turned out to be a trivial proof.
Wallis was born on November 23, 1616, to John and Joanna (nee Chapman) Wallis, residents of Ashford in Kent. In 1622, Wallis' father, a rector, died, and three years later young Wallis left Ashford in order to escape an outbreak of the plague. In 1625, he attended boarding school in Ley Green, near Tenterden, and after five years there he transferred to Martin Holbeach in Essex county. During one Christmas holiday Wallis asked his brother to introduce him to arithmetic and he mastered it in two weeks. It turned out Wallis was a "calculating prodigy," who could solve problems like the square root of a 53-digit number to 17 places without notation.
Wallis' education continued at Emmanuel College in Cambridge, where he studied medicine and wrote one of the first papers on the circulatory system. He also took courses in physics and moral philosophy, for which he was awarded a B.A. in 1637 and a fellowship to Queen's College. During this time, civil unrest was building in England. Wallis became a minister of the Church of England in 1640, serving as private chaplain in Yorkshire and Essex. He would also eventually become a royal chaplain to the court of Charles II and bishop of Winchester as well. Upon his marriage to Susanna Glyde in 1645 Wallis was forced out of his fellowship and moved to London. For his service in deciphering Royalist letters during the Civil War, Oliver Cromwell appointed Wallis Savilian Professor of Geometry at Oxford.
In 1655 Wallis produced his first major work, Arithmetica Infinitorum, which systematized the analytical methods of René Descartes and Bonaventura Cavalieri's method of indivisibles. It became a standard reference, influencing many mathematicians who thereafter wrote on the subject, and is still considered a monumental text in British mathematics. In 1658 Wallis was appointed an official archivist at Oxford, and in the following year his treatise on conics, Tractatus de sectionibis conicis, was published. In it, Wallis attempted to simplify Cartesian geometry--a notoriously recondite work--for consumption and use by his peers.
Among the vast range of mathematical subjects Wallis tackled included the quadrature of many curves, an infinite approximation for 4/, negative and fractional exponents, and calculating the center of gravity in cycloids by using indivisibles. He was the first to use the symbol to indicate infinity and the capital S for sine, and introduced the mantissa in logarithms. In his treatise on cycloids Wallis was the first to recast conic sections as curves of the second degree. His approximation for 4/, a formula now famous in mathematics, used "interpolation," a word peculiar to Wallis that became standardized.
Algebra: History and Practice, published in English in 1685, was significant not just as a historical document. Here, Wallis made the first recorded effort to graphically display the complex roots of a real quadratic equation. This intimated the geometric interpretations of complex numbers and trigonometry in use today in the Gaussian plane. He also prepared and published a second edition in 1693 as volume two of his Opera Mathematica. This enlarged version included the first systematic use of algebraic formulae--using numerical ratio to represent a given magnitude. That systematization had great impact on subsequent mathematical arguments about important unsolved problems in physics.
Wallis survived another political crisis, the Glorious Revolution (1688-1689), which led to the deposition of King James II. James' successor, William III, retained Wallis to decipher enemy communiques.
"Dueling Pamphlets"
Wallis wrote on subjects other than mathematics, including physics, theology, etymology and linguistics, general philosophy, and pedagogy. He is recognized as the first hearing person to systematize a means of teaching deaf mutes. Wallis was well known as a partisan; he successfully lobbied against the adoption of the Gregorian Calendar and was opposed to crediting Gottfried Wilhelm Leibnitz as a co-founder of the calculus. Wallis launched into an argument with the philosopher Thomas Hobbes, ostensibly regarding the subject of geometry. The two men traded insults in pamphlets with such florid titles as "Due Correction for Mr. Hobbes, or School Discipline for not saying his Lessons." Wallis married and had one son and two daughters. His wife died in 1687.
Wallis kept his post as Savilian Professor until his death at Oxford on October 28, 1703. Christopher Wren and Christiaan Huygens, inspired by Wallis' use of analogy in his writings, extended his investigations to the next generation of European mathematicians.
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